Dominik uses $20$ grams of filling for each dumpling he makes. He has $1500$ grams of dumpling filling. The grams $F$ of filling remaining is a function of $d$, the number of dumplings Dominik makes. Write the function's formula. $F=$
Solution: The amount of filling used to make each dumpling is constant, so we're dealing with a linear relationship. We could write the desired formula in slope-intercept form: $F= md+ b$. In this form, $ m$ gives us the slope of the graph of the function and $ b$ gives us the $y$ -intercept. Our goal is to find the values of $ m$ and $ b$ and substitute them into this formula. We know that each dumpling Dominik makes decreases the filling remaining by $20$ grams, so the slope $ m$ is ${-20}$, and our function looks like $F={-20}d+ b$. We also know that Dominik has $1500$ grams of filling initially, so the $y$ -intercept ${b}$ is ${1500}$. Since ${m}={-20}$ and ${b}={1500}$, the desired formula is: $F={-20}d+{1500}$